The rule of a table?

well...

if you go ahead and graph these points they appear to all be on a line.

So take a couple of them and figure out what the slope and intercept is and then double check that they all do lie on that line.

I get a slope of 3 and an intercept of -9 so the line the points lie on is

y=3x - 9

Checking this we get

1 -> -6

8 -> 15

10 -> 21

-20 -> -69

25 -> 66

and you can see that all the points lie on this line.

$$\begin{tabular}{|c|c|c|c|c|c|}
\hline
$x$&1&8&10&-20&25\\\hline
$y$&-6&15&21&-69&66\\\hline
\end{tabular}$$

Now I notice that the bottom numbers appear to be a bit less than 3 times the top ones.

so I am going to experiment with that;

$$\begin{tabular}{|c|c|c|c|c|c|}
\hline
$x$&1&8&10&-20&25\\\hline
$3x$&3&24&30&-60&75\\\hline
$y$&-6&15&21&-69&66\\\hline
\end{tabular}$$

Now I notice that 3x-9=y

So the rule is

$$y=3x-9$$

.